The derivative of 5x is 5.
I understand this expression to be 10x3 + 5x. Derivative: 30x2 + 5.
x = 10x, so derivative = 10
Derivative with respect to 'x' of (5x)1/2 = (1/2) (5x)-1/2 (5) = 2.5/sqrt(5x)
The idea is to use the addition/subtraction property. In other words, take the derivative of 5x, take the derivative of 1, and subtract the results.
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
The idea is to use the chain rule. Look up the derivative of sec x, and just replace "x" with "5x". Then multiply that with the derivative of 5x.
10 x
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
2.5x2 + any constant
9
20x -5
The derivative of f(x) is lim h-->0 [f(x+h)-f(x)]/h. So let f(x) = -5x. The derivative is lim h-->0 [-5(x+h)- -5(x)]/h = lim h-->0 [-5x - 5h + 5x]/h = lim h-->0 -5h/h Since the limit h-->0 of h/h is 1, the derivative is -5